It is common practice to inspect work pieces subsequent to production on a coordinate positioning apparatus, such as a coordinate measuring machine (CMM), in order to check for correctness of predefined object parameters, like dimensions and shape of the object.
In a conventional 3-D coordinate measurement machine, a probe head is supported for movement along three mutually perpendicular axes (in directions X, Y and Z). Thereby, the probe head can be guided to any arbitrary point in space of a measuring volume of the coordinate measuring machine and the object is measurable with a measurement sensor (probe) carried by the probe head.
In a simple form of the machine a suitable transducer mounted parallel to each axis is able to determine the position of the probe head and the provided probe relative to a base of the machine and, therefore, to determine the coordinates of a measurement point on the object being approached by the probe. For providing movability of the probe head a typical coordinate measuring machine may comprise a frame structure on which the probe head is arranged and driving means for moving frame components of the frame structure relative to each other.
For measuring surface variations, both measurement principles based on use of tactile sensors and of optical sensors are known.
In general, to provide a coordinate measuring machine with high measurement precision, its frame structure is therefore usually designed to have a high static stiffness. In order to achieve a stiff and rigid machine design, the frame structure or at least parts of it, is often made of stone, such as granite. Besides all the positive effects like thermal stability and good damping properties, the granite or other stiff materials also makes the machine and the movable frame elements quite heavy. The high weight on the other side also requires high forces for a decent acceleration.
However, weight reduction is a main topic relating to the designs of coordinate measuring machines, as if the machine components are built comprising less weight (and less stiffness) faster positioning of respective components can be achieved by causing fewer force affecting the coordinate measuring machine. On the other hand the influence of machine vibrations and torsions caused by reduced stiffness and (faster) movement of the machine components increase with weight reduction of these parts. Thus, uncertainties of derived measurement values and errors occurring from such deformations and vibrations increase accordingly. Therefore, especially with view to weight reduction but also for conventional machines, an accurate error handling is an important aspect.
For both approaches (heavy and light weight) an initial calibration procedure of the respective CMM is necessary particular for determining static and repeatable errors of the respective system. For maintaining stable and accurate measuring requirements, such a calibration preferably is to be executed in defined intervals due to taking account of external influences affecting the measuring system over time, e.g. changes of environmental parameters (temperature, humidity etc.) or mechanical impacts.
The calibration of a CMM may provide an improvement of a model which describes the static and/or dynamic behaviour of the CMM under certain conditions. Thereby, current calibration parameters may be used for actualising the defined model in order to more precisely—and adapted to current conditions—describe the behaviour of the CMM.
Typically, a so called compensation map is derived by the calibration procedure, wherein the map provides a compensation of each measuring value, which is acquired by measuring a measuring point of an object. Such a map may be designed as a kind of look-up table, i.e. for every coordinate or for defined coordinate steps of each axis of the CMM a corresponding compensated value is provided and an originally measured value is replaced by the compensated one. Alternatively, specified equations are determined and the equations are applied to measured position values for calculation of corresponding corrected values, thus providing a kind of compensation map.
Exemplarily for error handling, EP 1 559 990 discloses a coordinate measuring system and method of correcting coordinates measured in a coordinate measuring machine, measuring geometrical errors while parts with various weights are mounted on the coordinate measuring machine. Compensation parameters are derived from measured results per a weight of a part and stored. A compensation parameter corresponding to a weight of a part to be measured is appropriately read out to correct measured coordinates of the part to be measured.
As a further example, EP 1 687 589 discloses a method of error compensation in a coordinate measuring machine with an articulating probe head having a surface detecting device. The surface detecting device is rotated about at least one axis of the articulating probe head during measurement. The method comprises the steps of: determining the stiffness of the whole or part of the apparatus, determining one or more factors which relate to the load applied by the articulating probe head at any particular instant and determining the measurement error at the surface sensing device caused by the load.
Furthermore, the additional influence of the type of probe and of each probe for itself (due to given variations in probe assemblies) to be used for measurements may be considered. In the following, touch probes for taking tactile measurements are addressed.
FIG. 1a shows a typical touch trigger probe 100 known from prior art. The probe 100 comprises a touching element with a probe tip 101 for touching an object to be measured and determining a corresponding positional coordinate of the touched point at the object. Touch trigger probes like the one of FIG. 1a are commonly used with coordinate measuring machines (CMM) to evaluate the position of the axes indicated by contact of the probe tip with the object surface. Shown is a switching sensor. The stylus is attached to a tripod structure, whose three cylindrical arms 102 are supported by three pairs of crossed cylinders. It is a kinematics mechanism, which acts on the spring, thereby restoring the stylus to its original position.
In case the stylus touches an object and thus is deflected from its origin position a signal is provided by the cylindrical structures and indicates the deflection and with that the touching of the object.
FIG. 1b shows the typical error behaviour of a probe as shown in FIG. 1a. Due to the mechanical design of the probe, the trigger force is not constant in all directions and the resulting accuracy also looks correspondingly inhomogeneous, due to the fact that the bending of the stylus is a direct function of the force. Such error typically is also called “lobing error”. Here the lobing error for three directions is nearly or up to 5 μm.
The design of such probe and the behaviour of their lobing error are already known e.g. from Marek Dobosz and Adam Wozniak, “CMM touch trigger probes testing using a reference axis”, Precision Engineering 29 (2005) 281-289, or from A. Wozniak, M. Dobosz, “Metrological feasibilities of CMM touch trigger probes. Part I: 3D theoretical model of probe pretravel”, Measurement 34 (2003) 273-286.
In most use cases, today, the lobing error is considered to be constant in all directions, what is a quite strong limitation. An almost perfect reference sphere is used as a reference body to be measured for calibration and several points are measured around its equator, at its north pole (and sometimes in some other locations in between). The collected points are then supposed to be on a perfect sphere and a quadratic regression is used to calculate the diameter of the measured reference sphere. As a diameter of the reference sphere is provided like that, the stylus diameter easily can be calculated based thereon by use of the following formula:Dstylus=Dmeasured sphere−Dreference sphere 
This equation however would be perfect in the case the touch trigger probe behaviour would be absolutely homogeneous to all its touching directions, what is not the case in the real world. As a consequence of the above described approach, the calculate value Dstylus is used for all subsequent measurements, but as the lobing behaviour of the probe varies over the direction of touching an object, i.e. the angle of touching an object with respect to the probe, there is no exact direction-dependently compensated measuring value available. With other words, using a regression for determining the radius of the sphere and using such approximated values leads to mostly wrongly compensated measurements.
Moreover, the lobing effect can be reduced by use of a probe type which provides a more accurate triggering system (e.g. based on a piezo element). However, such probes are much more expensive than the commonly used simple probe type to which the description of above relates.
A further aspect to be considered as to possible errors to be compensated relates to the contact point between the touch probe and the surface of the object 103 to be measured. In fact, the exact contact point between the stylus tip 101 and the surface to be measured is not known. The software only assumes that the stylus motion (the speed vector 105) is perpendicular to the surface, when entering in contact. In the motorised mode (the CMM is driven with motors), when a CAD-model of the work piece is used, this can be achieved pretty accurately, but in the manual mode or when the work piece has relative big geometry errors or its location and orientation on the CMM is not exactly known, the exact contact point for a measuring point is inaccurate.
To better understand it, FIG. 2 shows the behaviour, where both the “considered contact point” 110 and the “real contact point” 111 are represented. The speed vector 105 shows the stylus direction before hitting the surface and the force vector 104 shows the work piece reaction when entering in contact.
As can be seen, as the exact contact point is not corrected, additional errors are generated when the stylus tip 101 does not touch the surface perfectly perpendicularly.